Finite Group Databasebeta

← Group #351122

Character table — Group #351122

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888224444444444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-11-1
χ41111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11-11
χ511111111111111111111111111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-11111-1-1111111-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-11111-1-11111-1-111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-222-2-22222-2-2-2-200200-2-200002-2-20000220000000000000000
χ182222222222-2-2-2-222-2-22222-2-2-2-200-200220000-2220000-2-20000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2222200200-2-200002220000-2-20000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2222200-200220000-2-2-20000220000000000000000
χ2122222222-2-22222-2-2-2-200000000222-2-22-222-2-2-2000000000000000000000000
χ2222222222-2-22222-2-2-2-20000000022-2-2-2-22-2-2222000000000000000000000000
χ2322222222-2-22222-2-2-2-200000000-2-22222-2-2-222-2000000000000000000000000
χ2422222222-2-22222-2-2-2-200000000-2-2-222-2222-2-22000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000000200-220000-2002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000000200-220000-200−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2220000000000-2002-200002002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2220000000000-2002-20000200−2i−2i2i2i002i2i−2i−2i000000000000
χ2922-22-2-22-22-222-2-22-22-20000000000000002i−2i2i−2i02i−2i2-22-22i−2i0000000000000000
χ3022-22-2-22-22-222-2-22-22-20000000000000002i−2i2i−2i0−2i2i-22-22−2i2i0000000000000000
χ3122-22-2-22-22-222-2-22-22-2000000000000000−2i2i−2i2i02i−2i-22-222i−2i0000000000000000
χ3222-22-2-22-22-222-2-22-22-2000000000000000−2i2i−2i2i0−2i2i2-22-2−2i2i0000000000000000
χ3322-22-2-22-22-2-2-2222-2-22000000002-202-200000002i−2i0000−2i2i2i−2i2i−2i000000000000
χ3422-22-2-22-22-2-2-2222-2-22000000002-202-20000000−2i2i00002i−2i−2i2i−2i2i000000000000
χ3522-22-2-22-22-2-2-2222-2-2200000000-220-2200000002i−2i0000−2i2i−2i2i−2i2i000000000000
χ3622-22-2-22-22-2-2-2222-2-2200000000-220-220000000−2i2i00002i−2i2i−2i2i−2i000000000000
χ3722-22-2-22-2-2222-2-2-22-222i2i−2i−2i2i2i−2i−2i00000002i−2i−2i2i0000000002-2-22000000000000
χ3822-22-2-22-2-2222-2-2-22-222i2i−2i−2i2i2i−2i−2i0000000−2i2i2i−2i000000000-222-2000000000000
χ3922-22-2-22-2-2222-2-2-22-22−2i−2i2i2i−2i−2i2i2i00000002i−2i−2i2i000000000-222-2000000000000
χ4022-22-2-22-2-2222-2-2-22-22−2i−2i2i2i−2i−2i2i2i0000000−2i2i2i−2i0000000002-2-22000000000000
χ4122-22-2-22-2-22-2-222-222-22i2i−2i−2i−2i−2i2i2i2-20-220000000002i−2i−2i2i000000000000000000
χ4222-22-2-22-2-22-2-222-222-22i2i−2i−2i−2i−2i2i2i-2202-2000000000−2i2i2i−2i000000000000000000
χ4322-22-2-22-2-22-2-222-222-2−2i−2i2i2i2i2i−2i−2i2-20-22000000000−2i2i2i−2i000000000000000000
χ4422-22-2-22-2-22-2-222-222-2−2i−2i2i2i2i2i−2i−2i-2202-20000000002i−2i−2i2i000000000000000000
χ454-444-4-4-44440000-4-4000000000000000000000000000000000000002i2−2i2000000
χ464-444-4-4-44440000-4-400000000000000000000000000000000000000−2i22i2000000
χ474-444-4-4-44-4-4000044000000000000000000000000000000000022−220000000000
χ484-444-4-4-44-4-40000440000000000000000000000000000000000−22220000000000
χ494-44-44-44-4004-44-400002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ504-44-44-44-4004-44-40000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ514-44-44-44-400-44-4400002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ524-44-44-44-400-44-440000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ534-4-4444-4-44-40000-440000000000000000000000000000000000002i2−2i200000000
χ544-4-4444-4-44-40000-44000000000000000000000000000000000000−2i22i200000000
χ554-4-4444-4-4-4400004-400000000000000000000000000000000000000002i2−2i20000
χ564-4-4444-4-4-4400004-40000000000000000000000000000000000000000−2i22i20000
χ574-4-4-4-4444004-4-44000022−22−222222−22−2222000000000000000000000000000000000000
χ584-4-4-4-4444004-4-440000−222222−22−222222−22000000000000000000000000000000000000
χ594-4-4-4-444400-444-4000022−22−2222−222222−22000000000000000000000000000000000000
χ604-4-4-4-444400-444-40000−222222−2222−22−2222000000000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ6288-8-88-8-88000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).